Question

Add : (3 root 2 + 7 root 3) and (root 2 - 5 root 3)

Answer 1

Answer:

$4\sqrt{2} +2\sqrt{3}$

Step-by-step explanation:

ATQ,

$(3\sqrt{2} +7\sqrt{3} ) + (\sqrt{2} -5\sqrt{3} )$

Firstly we open the brackets

$3\sqrt{2} +7\sqrt{3} +\sqrt{2} -5\sqrt{3}$

The way to add such numbers is to think of the radicals (root signs) as  variables.

Suppose,

$3a+a$

We simply add the coefficients of the same variable and get

$4a$

Similarly, we treat the radical signs and add their coefficients. So,

$\sqrt{2} (3+1) + \sqrt{3}(7-5)$

We get

$4\sqrt{2} +2\sqrt{3}$

Since difference variables e.g. a and b cannot be added unless specified, different radicals cannot be added, so we leave the expression as here.

Answer 2

Step-by-step explanation:

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